From what you say I would generally use a Shirley background over a linear background as this does attempt to mimic the electron loss processes (the background is an S-shape).
Tougaard’s formulation is very good, but usually works best over wider energy ranges than those we usually collect. CasaXPS, if you use that software, does have a variation on the full Tougaard method (U2 and U3 background types). More information on these can be found at http://www.casaxps.com and the associated YouTube channel
The choice of background plays a really important part in defining peak shapes too, for example, the Shirley background reduces asymmetry in the peak.
See also the Guru pages on backgrounds